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You can do one of the following things:
(1) select the references in Zotero and drag them into the WordPress edit window. Under Preferences (Gear icon) > Export you can select the output format and whether you want to copy as HTML or just plain text. I suggest you try both.
(2) create a bibliography (select refs and right-click in Zotero), save it as HTML, and then paste it into your WordPress page or post.
In general, the benefit of the Zotero HTML export is that it includes COinS. The problem is that it uses non-semantic markup for formatting, making it very difficult to adjust the layout to your liking.
A fix for that is in the making, I gather, but I have no idea when it actually will be implemented.
I would probably use something other than (or in addition to) WordPress to handle bibliographic data.
Diclaimer: I am a developer of 'refbase' that does this, but there are other web-based programs available & the upcoming Zotero server might solve some of your issues if you don't mind having it centrally hosted away from your site.
you may be interested in http://www.zotero.org/support/dev/oauth
Nice! Thanks for the tip. I'll see what I can do to integrate it.